一类特殊Riccati微分方程通解理论的分析及其统一  

Analysis and Unification of the General Solution Theory for a Class of Special Riccati Differential Equations

作　　者：赵临龙[1] Zhao Linlong(Ankang University,Ankang 725000,China)

机构地区：[1]安康学院,陕西安康725000

出　　处：《廊坊师范学院学报（自然科学版）》2024年第3期9-13,共5页Journal of Langfang Normal University(Natural Science Edition)

基　　金：陕西省科技厅研究项目(2022JM-050);陕西省一流课程“常微分方程”建设项目(2020-156);2022陕西省教育科学研究项目(SGH22Y1458)

摘　　要：Riccati微分方程在实际工程中有着广泛的应用,但由于不可积的特性,使其解法具有挑战性。针对相关文献中有关Riccati微分方程通解的问题,利用Riccati微分方程的不变量关系式进行分析讨论,揭示该微分方程解的内在本质,并且将相关文献中的Riccati微分方程解法统一起来,达到求解的简单美。Riccati differential equations are widely used in practical engineering,but their non-integrable characteristics make their solution challenging.Aiming at the problem of the general solution of Riccati differential equation in the relevant literature,this paper uses the invariant relation of Riccati differential equation to analyze and discuss,reveals the inherent nature of the solution of the differential equation,and unifies the solution of Riccati differential equation in the relevant literature,so as to achieve the beauty of solving simply.

关 键 词：RICCATI微分方程 不变量 可积类型 统一性 

分 类 号：O174.2[理学—数学]